Modular elimination in matroids and oriented matroids

Delucchi, Emanuele (2011) Modular elimination in matroids and oriented matroids. European Journal of Combinatorics, 32 (3). pp. 339-343. ISSN 01956698

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Abstract

We introduce a new axiomatization of matroid theory that requires the elimination property only among modular pairs of circuits, and we present a cryptomorphic phrasing thereof in terms of Crapo’s axioms for flats. This new point of view leads to a corresponding strengthening of the circuit axioms for oriented matroids.

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